Solve for x. Please show work.

Answer:

160.0 cm²  

Step-by-step explanation:

R = 42 cm; s = 44 cm

1. Central angle θ (working in radians)

θ = s/R

θ = 44/42

θ = 22/21

===============

2. Area of sector

A = ½R²θ

A = ½(42)²(22/21)

A = ½(42×21×2)(22/21)

A = 924 cm²

===============

3. Area of triangle

A = ½R²sinθ

A = ½(42)²sin(22/21)

A = ½ ×1764 × 0.8662

A = 764.0 cm²  

===============

4. Area of segment

Area of segment = Area of sector – area of triangle

= 924 – 764.0

= 160.0 cm²

The area of segment is [tex]\boxed{160{\text{ c}}{{\text{m}}^2}}.[/tex]

Further explanation:

The formula of angle can be obtained as follows,

[tex]\boxed{\theta= \frac{{{\text{arc}}}}{{{\text{radius}}}}}[/tex]

The formula for area of sector can be expressed as follows,

[tex]\boxed{{\text{Area of sector}} = \frac{1}{2}{r^2}\theta }[/tex]

The formula for area of triangle can be expressed as follows,

[tex]\boxed{{\text{Area of triangle}} = \frac{1}{2}{r^2}\sin \theta }[/tex]

Given:

The radius of the circle is [tex]42{\text{ cm}}.[/tex]

The length of an arc is [tex]44{\text{ cm}}.[/tex]

Explanation:

The radius of the sector is [tex]42{\text{ cm}}[/tex] and the length of an arc is [tex]44{\text{ cm}}.[/tex]

The angle can be obtained as follows,

[tex]\begin{aligned}\theta&= \frac{l}{r}\\&=\frac{{44}}{{42}}\\&= \frac{{22}}{{21}}\\\end{aligned}[/tex]

Area of the triangle can be obtained as follows,

[tex]\begin{aligned}{\text{Area}}&= \frac{1}{2}{r^2}\sin {{\theta }}\\{\text{ }}=&\frac{1}{2}{\left( {42} \right)^2}\sin \left( {\frac{{22}}{{21}}} \right) \\&=882 \times 0.8662\\&=764{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]

Area of sector can be obtained as follows,

[tex]\begin{aligned}A&= \frac{1}{2}{r^2}\theta\\&= \frac{1}{2} \times {\left( {42} \right)^2} \times \left({\frac{{22}}{{21}}} \right) \\&= 924{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]

The area of segment can be obtained as follows,

[tex]\begin{aligned}{\text{Area of segment}}&= {\text{Area of sector}} - {\text{Area of triangle}}\\&= {\text{924}} - 764\\&= 160{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]

The area of segment is [tex]\boxed{160{\text{ c}}{{\text{m}}^2}}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Area of Circles

Keywords: area, minor segment, circle, radius 42 cm, length of the corresponding arc is 44 cm, sector, segment.

Answer:

B. g/cm3

Step-by-step explanation:

Answer:

kilogram

Step-by-step explanation:

The SI unit of kilogram per cubic metre (kg/m3) and the cgs unit of gram per cubic centimetre (g/cm3) are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. (The cubic centimeter can be alternately called a millilitre or a cc.)

Answer:

12(2v - 7)

Step-by-step                

Answer: 25%

Step-by-step explanation:

Given : The price of a video game was reduced from $60 to $45.

i.e. Previous price = $60

New price = $45

Reduction in price = Previous price -New price

= $60 - $45 = $15

Then, the percentage was the price of the video game reduced :-

[tex]\dfrac{\text{Reduction in price}}{\text{Previous price}}\times100\\\\=\dfrac{15}{60}\times100=25\%[/tex]

Hence, the percentage was the price of the video game reduced = 25%

25% was the price of the video game reduced.

Step-by-step explanation:

Given :

Previous Price of the video game = $60

Present Price of the video game = $45

Calculation :

Let previous price of the video game be 100% than,

[tex]= \dfrac{45\times 100}{60}[/tex]

=  75%

Reduced Percentage = 100 - 75 = 25%

Therefore,  25% was the price of the video game reduced.

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Answer: If the question you are asking is how many meters Tracy ran per minute the answer would 200 meters per minute

Step-by-step explanation:

1) You would take 1,000 and divide it by 5

In order to check your work you can just multiply 200 by 5.

Hope this helped!

256 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

       = 2⁸

16 = 2 * 2 * 2 * 2

   = 2⁴

Answer: choice (3)

Open circle at -2; shading to the right of -2

==============================

Work Shown:

-2x+8 < 12

-2x+8-8 < 12-8 ... subtract 8 from both sides

-2x < 4

-2x/(-2) > 4/(-2) ... divide both sides by -2; sign flips

x > -2

To graph this, plot an open circle at -2 on the number line. Shade to the right of this open circle. The open circle means "this value is not included in the shaded solution region". The sign flips in the second to last step because we divided both sides by a negative number.

Answer:

3.     x>-2  see graph

Step-by-step explanation:

-2x+8 < 12

Subtract 8 from each side

-2x+8 -8 <12-8

-2x <4

Divide by -2 (Remember this flips the inequality)

-2x/-2 > 4/-2

x >-2

Answer:

-2x-4

Step-by-step explanation:

(-7x-7y-4)-(-5x-7y)=-7x-7y-4+5x+7y=-7x-4+5x=-2x-4

Answer:

-2x - 4

Step-by-step explanation:

Answer:

x = 1 , y = 1 and z = 0

Step-by-step explanation:

-2x+2y+3z=0    ------(1)

-2x-y+z=-3     --------(2)

2x+3y+3z=5    ---------(3)

To find the values of x,y and z

(3) - (2)⇒ 2y + 4z = 2

y + 2z = 1   --------(4)

(1) - (2)⇒ 3y +2z =3   ---(5)

(5) - (4)⇒ 2y = 2

y = 1

Substituting the value of y in (4) we get z =0

Substituting the value of y and z  in (1) we get x = 1

Therefore x = 1 , y = 1 and z = 0

Answer:

x = $3

y = $4

Step-by-step explanation:

We need to know the prices of gravel and peas. We can find the price by using equations and graphing them.

Let X be the price of the sand

Be and the price of pea gravel

In the first purchase we have:

[tex]4x + 3y = 24[/tex]

In the second purchase we have

[tex]2x = 6[/tex]

Both relations represent the equation of a line. In the graphic shown, these lines are drawn. In this case the interception between both lines represents the price of each product, and the solution of the problem. You can see that the lines intersect at point (3 4). This means that the price of each bag of sand is $ 3, and the price of a bag of pea gravel is $ 4.

Answer:

3 miles per hour

Step-by-step explanation:

If you walk 1.5 miles in .5 of an hour you take 1.5 and divide it by .5 of an hour and you get the speed you were walking

Answer:

3 miles per hour

Step-by-step explanation:

Answer:

x=8.4

Step-by-step explanation:

4x + 8 (0.8) = 40

4x = 40 - 6.4

4x = 33.6

x = 33.6/ 4

x= 8.4

B) 8.4..............

The student's final grade in the class is 87.08%.

Calculating the Student's Final Grade:

Step 1: Calculate Individual Category Scores:

Tests: 90% (average)

Quizzes: (67 + 90 + 44 + 29 + 100 + 100 + 100) / 7 = 78.43%

Homework: 85% (average)

Final Exam: 98%

Step 2: Apply Category Weights:

Tests: 90% * 55% = 49.5%

Quizzes: 78.43% * 30% = 23.53%

Homework: 85% * 5% = 4.25%

Final Exam: 98% * 10% = 9.8%

Step 3: Add Category Scores:

49.5% + 23.53% + 4.25% + 9.8% = 87.08%

Therefore, the student's final grade in the class is 87.08%.

Answer:

16 nickels thicker

Step-by-step explanation:

You would need 20 nickels for 1 dollar and only 4 quarters for 1 dollar.  Do 20 minus 4 and your answer is 16 nickels. The stack of nickels is 16 coins thicker. Hope this helped!

Answer:

slope of y = -7 is 0

Step-by-step explanation:

y = any number forms a graph of a horizontal line

x = any number forms a graph of a vertical line

For any horizontal line , the slope is always 0

for any vertical line  , the graph is always undefined

So for y =-7 we will get a horizontal line at -7  on t

the slope of horizontal line y=-7 is 0

The IQ score that aligns with a z-score of 2.33 in a normal distribution having a mean of 100 and a standard deviation of 15 is approximately 135.

The IQ score that corresponds to a z-score of 2.33 can be found using the z-score equation. In this equation, z is equal to (X - μ)/σ, where X is the value we're trying to find, μ is the mean, and σ is the standard deviation. Given that the mean (μ) is 100 and the standard deviation (σ) is 15, we can plug these values into the equation along with the z-score of 2.33 to solve for X. Through rearrangement of the z-score equation, X = zσ + μ. Substituting a z of 2.33, σ of 15, and μ of 100, gives X = (2.33*15) + 100 = 134.95. Hence, an IQ of approximately 135 corresponds to a z-score of 2.33 on a normally distributed IQ test.

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Answer:

The answer is 13/7

Step-by-step explanation:

Answer:

13/7

Step-by-step explanation:

3 arrays - 1 x 9 (or 9 x 1) and 3 x 3

Hence, the number of arrays = 2 x 2 = 4 = even

First, we pair the different factors of 9.

The different factors of 9 are:

(1, 9) and (3, 3)

For each pair, Mr. Deets can make 2 arrays.

So, the total number of arrays that Mr. Deets can make = 2 x 2 = 4 and hence the number of arrays is even.

Answer:

4 arrays,

Number of arrays is even.

Step-by-step explanation:

∵ The possible pairs of two numbers which give 9 after multiplication,

( 3, 3) and (9, 1),

So, the possible array would be,

3 × 3, 9 × 1

Note : 9 × 1 can also be written as 1 × 9,

According to the question,

For each pair of different factors, there are two arrays,

3 × 3 and 9 × 1 are two arrays with no same factor,

Hence, the total arrays = 2 × 2 = 4

Which is an even number.

Answer:

If you want me to solve for b then

b  ≤  − 6

The solution to the given inequality is b≤-6.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -1.2b-5.3≥1.9.

Add 5.3 on both the sides of an inequality, we get

-1.2b≥7.2

Divide -1.2 on both the sides of an inequality, we get

b≤-6

In  interval notation: (-∞,-6]

Therefore, the solution is b≤-6.

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Answer:

No, there is not enough water.

Step-by-step explanation:

The water bottle holds 24.5  and there is 3/5 of it.

3/5 of 24.5 is 14.7 ounces

You want to fill three glasses with 5 ounces each. Multiply 3 x 5 which gives you 15.

14.7 is less than 15

Subtract 15 from 14.7 and you'll have a negative or not enough so no, it cannot fill three glasses with 5 each.

The possible widths of the room go from 8 to 27 feet, as well as the possible lengths of it.

Given that a rectangular room must have a perimeter of 70 feet and an area of at least 200 square feet, to determine the possible widths of the room the following calculations must be performed:

Rectangle = 70 feet of perimeter = 35 feet of base and height added

Area of a rectangle = base times height

Therefore, the possible widths of the room go from 8 to 27 feet, as well as the possible lengths of it.

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Answer:

0.375 or 37.5%

Step-by-step explanation:

To do this you divide 8 by 3 because he has 3 colored socks out of 8 socks.

Answer:

z=5

Step-by-step explanation:

1/4=z/20

20*1/4=z

z=5

Answer:17/20

Step-by-step explanation:

100% being a whole.

so she got 85% out of 100%, then 85 out of 100.

[tex]\bf \cfrac{85}{100}\implies \cfrac{5\cdot 17}{5\cdot 20}\implies \cfrac{5}{5}\cdot \cfrac{17}{20}\implies 1\cdot \cfrac{17}{20}\implies \cfrac{17}{20}[/tex]

Answer:

$10,200

Step-by-step explanation:

12,000x 0.85 = $10,200

or 12,000 x 0.15 = 1,800

$12,000 - $1,800 - $10,200

Answer:

could you be more specific? link doesn't take me anywhere

Answer:

Step-by-The GCF of 35 and 63 is 7. To find the GCF, we will start by listing the factors of 35 and listing the factors of 63. We see that the factors that are common to both 35 and 63 are 1 and 7, and the greatest of these is 7. Therefore, the greatest common factor of 35 and 63 is 7.step explanation:

The greatest common factor of the numbers 35 and 63 will be 7.

We may use the prime factorization method to get the greatest common factor (GCF) of 35 and 63.

The two numbers are first factored into their prime factors.

While 63 can be written as 3 * 3 * 7, 35 may be written as 5 * 7.

Next, we determine the common prime factors and calculate each factor's lowest exponent.

The common component in this instance is 7. The GCF of 35 and 63 is thus 7.

The greatest number that divides both 35 and 63 without producing a remainder is the GCF.

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